By Cooper J.A., Goldreich O.
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Minimum Time for a Hybrid System with Thermostatic Switchings Fabio Bagagiolo Dipartimento di Matematica, Universit` a di Trento, Via Sommarive 14, loc. it Abstract. In this paper we study a minimum time problem for a hybrid system subject to thermostatic switchings. We apply the Dynamic Programming method and the viscosity solution theory of Hamilton-Jacobi equations. We regard the problem as a suitable coupling of two minimumtime/exit-time problems. Under some controllability conditions, we prove that the minimum time function is the unique bounded below continuous function which solves a system of two Hamilton-Jacobi equations coupled via the boundary conditions.
Springer Verlag, pp. 480-494 (March 2005). 9. : Neuro-Dynamic Programming. Athena Scientiﬁc, Belmont, MA (1996). edu Abstract. The aim of this paper is twofold. On one hand we present an approach to the general problem of nonlinear control in the framework of (diﬀerentiable) groupoids, which, in our opinion deserves further investigation. On the other hand, using recently-developed algebraic tools, we show that for a control system whose state space is a semisimple Lie group (like SO(3)), it is possible to reach a dense subset of the state space using just two properly chosen discrete controls, and this property is robust with respect to the choice of controls.
A. Bicchi, A. Marigo, and B. Piccoli. On the reachability of quantized control systems. IEEE Trans. on Automatic Control, 47(4), April 2002. 3. A. Marigo and A. Bicchi. Steering driftless nonholonomic systems by control quanta. In Proc. IEEE Conf. on Decision and Control, 1998. 4. A. Bicchi, Y. Chitour, and A. Marigo. Reachability and steering of rolling polyhedra: a case study in discrete holonomy. , 49(5), May 2004. 5. R. W. Brockett. Formal languages for motion description and map making. In R.